If you analyze this table closely, it becomes very clear that the two main factors in search engine ranking according to Moz are: social media engagement (number of likes, pluses, etc) and back links, i.e. unique domains linking to your website. Needless to say, "back links" these days always means "quality back links" - links from websites in your industry or from generally recognized reputable websites (news, radio, industry magazines, etc).
We fully agree with these two factors - they are hardly a surprise to anyone who has been doing SEO for years. I am surprised it took that long for social media to begin to factor in SEO.
There is a couple of items listed by Moz where our findings do not correspond. Remember, SEO is an empirical trade, i.e. nobody knows anything for sure except Google, so your experience and observations are just as good as anyone else's.
According to Moz, keywords in the Title tags and H1 tags no longer have a high value. We find, however, that the keywords in the Title tags and H1 tags still do matter, but not as much as before. However, over-optimization is counterproductive, in that, repeating your keywords more than once in one Title or one H1 tag is likely to produce an adverse effect. We tested this on one of our websites and after "de-optimizing" the site, the site went up in ranking by several links. We made sure to do one thing at a time and leave two weeks between each new step.
Likewise, Moz states that external links value very little. But we find that external links play a noticeable role, actually. Those are the links that you provide on your pages to other websites. After adding 30 quality external links on various pages, including 4-5 on the home page, one of our website went up on Google by several links.
In addition, we find that content - and lots and lots of it - plays a definite role in search engine ranking. Long descriptive articles, with 1000+ words per article, with nice formatting and images will move your site up gradually. Just ensure that you enable Google authorship and publish article under your name, so that your profile being to accrue authority.